Group theory and generalizations Representation theory of groups Concept
Irreducible representation
Summary
An irreducible representation is a nonzero group representation with no proper nonzero invariant subspace. Irreducible representations are the building blocks of representation theory. For a finite group over the complex numbers, every finite-dimensional representation is a direct sum of irreducible ones, by Maschke's theorem.
Where this leads
29 pages build on this one.
- Weyl character formula for compact groups
- Unitary dual
- Discrete series representation
- Wigner D-matrix
- Representation theory of SL2(R)
- Brauer's height zero conjecture
- Principal series representation
- Representation theory of the symmetric group
- Peter–Weyl theorem
- Theta correspondence
- Representation theory of SU(2)
- Pariah groups
- 3-j symbol
- Schur orthogonality relations
- Harish-Chandra module
- Monster group
- Gelfand–Raikov theorem
- Monstrous moonshine
- Admissible representation
- Wigner's classification
- Schur orthogonality for compact groups
- Borel–Weil–Bott theorem
- Character table
- Complete reducibility of representations of compact groups
- Janko groups
- Representation theory of the Lorentz group
- Clifford theory
- Baby Monster group
- McKay conjecture
Further reading
About this page
| Tag | FX3NEFYFFN |
|---|---|
| URI | m2://FX3NEFYFFN |
| Kind | concept |
| Writing | W0 stub |
| MSC | 20C15 |
| Specializes | Group representation |
| Same as |
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Used by
- Weyl character formula for compact groups
- Unitary dual
- Discrete series representation
- Wigner D-matrix
- Representation theory of SL2(R)
- Brauer's height zero conjecture
- Principal series representation
- Representation theory of the symmetric group
- Peter–Weyl theorem
- Theta correspondence
- Representation theory of SU(2)
- 3-j symbol
- Schur orthogonality relations
- Harish-Chandra module
- Monster group
- Gelfand–Raikov theorem
- Admissible representation
- Wigner's classification
- Schur orthogonality for compact groups
- Borel–Weil–Bott theorem
- Character table
- Complete reducibility of representations of compact groups
- Representation theory of the Lorentz group
- Clifford theory
- McKay conjecture